Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2011 AMC 10B Problems/Problem 8"

m (see also)
m
Line 1: Line 1:
−
== Problem 8 ==
+
== Problem==
  
 
At a certain beach if it is at least <math>80^{\circ} F</math> and sunny, then the beach will be crowded. On June 10 the beach was not crowded. What can be concluded about the weather conditions on June 10?
 
At a certain beach if it is at least <math>80^{\circ} F</math> and sunny, then the beach will be crowded. On June 10 the beach was not crowded. What can be concluded about the weather conditions on June 10?

Revision as of 17:12, 4 June 2011

Problem

At a certain beach if it is at least $80^{\circ} F$ and sunny, then the beach will be crowded. On June 10 the beach was not crowded. What can be concluded about the weather conditions on June 10?

$\textbf{(A)}\ \text{The temperature was cooler than } 80^{\circ} \text{F and it was not sunny.}$

$\textbf{(B)}\ \text{The temperature was cooler than } 80^{\circ} \text{F or it was not sunny.}$

$\textbf{(C)}\ \text{If the temperature was at least } 80^{\circ} \text{F, then it was sunny.}$

$\textbf{(D)}\ \text{If the temperature was cooler than } 80^{\circ} \text{F, then it was sunny.}$

$\textbf{(E)}\ \text{If the temperature was cooler than } 80^{\circ} \text{F, then it was not sunny.}$

Solution

$C, D,$ and $E$ can not be right because the sun intensity of June 10 does not depend at all on the temperature.

If it was cooler than $80^\circ$ but it was still sunny, it would not meet the conditions of $A,$ but the beach would still be not crowded.

However, $B$ means that if either condition was not met, then the beach would not be crowded. Therefore, the correct answer is $\boxed{\textbf{(B)}}$

See Also

2011 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_10B_Problems/Problem_8&oldid=39174"